Saturday, August 11, 2012

Representations Arithmetical and Topological

Representations Arithmetical and Topological

L. Edgar Otto    Friday, 10 August, 2012

At the end of my allotted time this morning positing from the Eau Claire WI (the 30 state in the Union hence my artful preoccupation with the arrangement of stars into fivefold symmetry) after posting I checked this sci magazine article that shows a computer generated Venn diagram of eleven arguments.

Now, a linear notation, a single diamond in the illustration, in the sense of adding one is also the possibility or process of doubling the elements involved (methods of complex numbers aside to show this) as with Louis Carrol's algebraic and structural Venn like diagrams when extend to 32 objects for example.  So the question is how far can we extend the symmetry of these views.  Eleven being significant in the Fibonacci loops recalls the adding (or subtracting) of one of the Mersennes as in Pitkanen's hadron which amounts to a physical embodiment of these logical notations as with the number 89 and its mirror inverse.

Yet, I am reminded again that early on the four symmetry of the DNA coding as a quasic plane is a matter of this Venn like but intelligibly ordered topologically, logic.  In as sense the philosophic logic tends to use the same general pattern as a matter of symmetries, hidden or overt, in the world or our dreams.

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